[FIX] Nomogram: Use softmax for multinomial logistic regression

[MohammadHijjawi97]

Issue

Fixes #7326

Description of changes

Logistic regression on data with more than two classes is multinomial and computes its probabilities with softmax. The nomogram instead turned the target class's points into a probability with a per-class sigmoid, optionally normalized by the sum of the sigmoids, so the displayed probabilities did not match the model's predictions. For example, for iris[53] the model gives 2/94/5 % but the nomogram showed 15/92/34 %.

• For multiclass logistic regression, the probabilities and the probability scale are now computed with softmax over the totals of all class values. This uses the existing __get_totals_for_class_values helper.
• The total ruler now covers all reachable totals. Before, the dot was clipped for confident predictions (iris[0] showed 47 % while the model gives 98 %).
• The "Normalize probabilities" checkbox is hidden for logistic regression, since softmax probabilities already sum to 1.
• Naive Bayes and binary logistic regression are unchanged.

Tests:

• Added test_probabilities_lr_multiclass: for several iris instances, both scales and every target class, the displayed probability equals cls(inst, cls.Probs), and the ruler covers the total.
• Updated the expected values in test_nomogram_lr_multiclass from [18, 56, 78], which summed to 152 %, to [4, 25, 70]. These are the model's predict_proba at the marker position (0.0439 / 0.2533 / 0.7027).

I also compared the nomogram with the model across instances of iris, zoo and heart_disease, with both scales and with 5 or all features. After the fix they agree to within 1 %.

Note: I tested on Windows against the 3.40.0 wheel. There, a few existing nomogram tests fail the same way before and after this change, because the hidden widget is narrow and the ruler collapses. With the widget sized to 1400x900 they pass. I couldn't check the new expected values in test_nomogram_lr_multiclass with CI's default widget size, so please check that one in CI.

Includes

• Code changes
• Tests
• Documentation

[CLAassistant]

All committers have signed the CLA.

[codecov]

Codecov Report

❌ Patch coverage is 95.45455% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 89.02%. Comparing base (4d54417) to head (5a74093).
⚠️ Report is 1 commits behind head on master.

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #7331      +/-   ##
==========================================
+ Coverage   88.99%   89.02%   +0.03%     
==========================================
  Files         337      337              
  Lines       74598    74614      +16     
==========================================
+ Hits        66387    66427      +40     
+ Misses       8211     8187      -24     

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[VesnaT]

Thank you for the fix. It looks promising, but I found a few issues:

1. With the points scale and some features hidden, the nomogram shows probabilities that don't match the model.

2. With the points scale and some features hidden, the nomogram shows probabilities that don't match the model.

3. When the target class has zero coefficients, (use L1) the nomogram shows wrong probabilities.

4. When there are two classes with zero coefficients, the nomogram crashes.